Oberwolfach Surgery Seminar 2012: General information
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=== Algebraic surgery versus geometric surgery === | === Algebraic surgery versus geometric surgery === | ||
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<li>[[Oberwolfach Surgery Seminar 2012: Program#The algebraic surgery exact sequence|The algebraic surgery exact sequence]] [[User:Ranicki|AR]] | <li>[[Oberwolfach Surgery Seminar 2012: Program#The algebraic surgery exact sequence|The algebraic surgery exact sequence]] [[User:Ranicki|AR]] | ||
<li>[[Oberwolfach Surgery Seminar 2012: Program#The topological block bundle obstruction|The topological block bundle obstruction]] [[User:Tibor Macko|TM]] | <li>[[Oberwolfach Surgery Seminar 2012: Program#The topological block bundle obstruction|The topological block bundle obstruction]] [[User:Tibor Macko|TM]] | ||
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<li>[[Oberwolfach Surgery Seminar 2012: Program#Examples and related developments|Examples and related developments]] [[User:Diarmuid Crowley|DC]], [[User:Tibor Macko|TM]], [[User:Ranicki|AR]] | <li>[[Oberwolfach Surgery Seminar 2012: Program#Examples and related developments|Examples and related developments]] [[User:Diarmuid Crowley|DC]], [[User:Tibor Macko|TM]], [[User:Ranicki|AR]] | ||
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| + | == Examples == | ||
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| + | <li>[[Oberwolfach Surgery Seminar 2012: Program#Examples of non-smoothable Poincaré complexes|Examples of non-smoothable Poincaré complexes]] [[User:Martin Olbermann|Martin Olbermann]], [[User:Steve Balady|Steve Balady]], [[User:Winges|Christoph Winges]], [[User:Ranicki|AR]]</li> | ||
== Schedule == | == Schedule == | ||
Revision as of 09:45, 1 June 2012
Contents |
1 Prerequisites
The prerequisites for the seminar are a solid knowledge of the basics of differential and algebraic topology, meaning: manifolds, Poincaré duality, bundles, cobordism, transversality, generalized homology and cohomology, homotopy groups.
Participants should be familiar with the ideas covered in the first 7 chapters of the book [Ranicki2002]. However material from sections 2.2., 4.2, 5.4, 7.3 will be covered during the seminar. In addition participants should be familiar with the basics of spectra in stable homotopy theory. A good reference here is [Hatcher2002, Section 4.F].
The main references for the material covered in the seminar are [Ranicki1979], [Ranicki1992], [Kühl&Macko&Mole2011] and [Wall1999].
2 Program
2.1 Geometric surgery
- Bundle theories DC
- Spivak normal fibration DC
- Normal invariants and surgery below the middle dimension DC
- Immersions, the Wall form and formations DC
- L-groups and Wall realisation DC
- The geometric surgery exact sequence DC
- The TOP surgery exact sequence TM
2.2 Algebraic surgery
- Structured chain complexes AR
- Symmetric and quadratic signature AR
- Algebraic surgery and L-groups via chain complexes AR
- Additive categories with chain duality and categories over complexes TM
- Generalized homology theories TM
- The normal complexes TM
2.3 Algebraic surgery versus geometric surgery
- The algebraic surgery exact sequence AR
- The topological block bundle obstruction TM
- The surgery obstruction TM
- The geometric and algebraic surgery exact sequences AR
- Examples and related developments DC, TM, AR
3 Examples
- Examples of non-smoothable Poincaré complexes Martin Olbermann, Steve Balady, Christoph Winges, AR
- 9.00 - 10.00 Lecture 1 (DC)
- 10.20 - 11.20 Lecture 2 (DC)
- 11. 30 - 11.55 Exercise session 1
- 12.00 - 13.00 Lunch
- 13.00 - 14.30 Afternoon break
- 14.30 - 15.30 Lecture 3 (DC)
- 15.50 - 16.50 Lecture 4 (DC)
- 17.00 - 18.00 Exercise session 2
- 9.00 - 9.30 Special memorial lecture in honour of Hirzebruch (AR)
- 9.30 - 10.30 Lecture 5 (DC)
- 10.50 - 12.15 Lecture 6 (DC)
- 12.15 - 12.30 Photo
- 12.30 - 13.30 Lunch
- 13.30 - 15.00 Afternoon break
- 15.00 - 16.00 Lecture 7 (TM)
- 16.20 - 17.20 Lecture 8 (AR)
- 17.30 - 18.15 Exercise session 3
- 9.00 - 10.00 Lecture 9 (AR)
- 10.20 - 11.20 Lecture 10 (AR)
- 11. 30 - 12.15 Exercise session 4
- 12.30 - 13.30 Lunch
- 13.30 - 18.30 Free afternoon
- 20.00 - 22.00 Lecture 11 - Examples of Poincaré complexes (Martin Olbermann, Steve Balady, Christoph Winges, AR)
- 9.00 - 10.00 Lecture 12 (TM)
- 10.20 - 11.20 Lecture 13 (TM)
- 11.30 - 12.15 Exercise session 5
- 12.30 - 13.30 Lunch
- 13.30 - 15.00 Afternoon break
- 15.00 - 16.00 Lecture 14 (TM)
- 16.20 - 17.20 Lecture 15 (AR)
- 17.30 - 18.15 Exercise session 6
- 20.00 - 20.30 Film of Browder's retirement lecture
- 21.00 - 22.00 Piano concert by Marek Kaluba and Carmen Rovi
- 9.00 - 10.00 Lecture 16 (AR)
- 10.20 - 11.20 Lecture 17 (TM)
- 11.30 - 12.15 Exercise session 7
- 12.30 - 13.30 Lunch
- 13.30 - 15.00 Afternoon break
- 15.00 - 16.00 Lecture 18 (TM)
- 16.20 - 17.35 Lecture 19 (DC, TM, AR)
- 17.40 - 18.25 Exercise session 8
